This invention relates to improvement or resynchronization of phase reference signals in signal demodulation or decoding arrangements.
Trellis decoders or demodulators are used to demodulate signals modulated by continuous phase modulation (CPM). In the context of the present invention, coding/decoding and modulation/demodulation are analogous, and may be viewed as corresponding. The CPM modulation scheme has the advantage of providing a signal having substantially constant power, which is a marked advantage when transmitting the modulated signals over a nonlinear channel, as constant power tends to reduce the generation in such a channel of unwanted distortion products which obscure the signals. A further advantage of CPM modulation is that the bandwidth of the signal is easily maintained, and the frequency spectrum exhibits low sidelobes, which is advantageous for situations in which a plurality of signals traverses a channel, as the signal spectrum for one of the signals traversing the channel has little frequency overlap with the signal next adjacent in frequency.
CPM modulation is performed, in general, by converting the information or signal to mxe2x88x92ary quantized form, if not already in the desired form. For the simple case in which m=1, the signal is converted into binary form. The mxe2x88x92ary signal is applied to a shift register array having a particular length. As the signal bits are applied to the input end of the shift register array, the previously-applied signals propagate through the register array, altering the states of the registers in succession. A combinatorial or functional logic arrangement is coupled to the output of each register of the array, and applies some function to the combination of register logic states, which function results in one or more output signals, which depend upon the combinatorial function, and also depend upon the current state of each register of the array, which in turn depends upon the history of the input signal.
The demodulation of a signal modulated in the abovedescribed fashion may be accomplished by a trellis demodulator. The xe2x80x9ctrellisxe2x80x9d represents, by xe2x80x9cnodesxe2x80x9d, the possible states of the registers of the modulator, and by lines joining the nodes the possible paths by which transitions between states can be made. The trellis demodulator is often implemented as a Viterbi algorithm which performs sequence detection on the received symbol sequence. Demodulation using a Viterbi algorithm requires an accurate estimate of the phase of the carrier signal with respect to the transmitter reference phase. The process of obtaining an accurate estimate is known as carrier phase synchronization.
The appropriate likelihood function L(t, xcex8, xcfx84, D) for estimating the carrier phase is defined by equation (1) of FIG. 1, where N0 is the noise power, T0 is the observation interval, y(t) is the received signal, C is a constant responsive to the amplitude of the received signal, and s(t, xcex8, xcfx84, D) is the transmitted signal. The parameters of the transmitted signals are xcex8, the carrier phase; xcfx84, the symbol timing reference, and D, the transmitted data sequence. Taking logarithms and expanding the squared term in equation (1) gives the log-likelihood function l(t, xcex8, xcfx84, D) as set forth in equation (2) of FIG. 1.
The constant first term of equation (2) of FIG. 1 and the second term within the integral of equation (2) of FIG. 1 are independent of the parameter xcex8 of interest and can be dropped. For a constant envelope scheme such as CPM, the first term within the integral of equation (2) is also independent of the carrier phase reference xcex8. The equivalent log-likelihood function l (t, xcex8, xcfx84, D) to be maximized is therefore given by equation (3) of FIG. 1.
A necessary condition for a maximum of the equivalent log-likelihood function of equation (3) of FIG. 1 is that the derivative be zero at the maximum. Differentiating equation (3) with respect to the carrier phase reference xcex8, and setting the result equal to zero, gives likelihood equation (4) of FIG. 1.
The transmitted signal in a CPM arrangement can be expressed as s(t, xcex8, xcfx84, D) in equation (5), where D is a vector, E is the transmit energy, T is the symbol period, xcfx890 is the carrier frequency, and D=(dxe2x88x92∞, . . . dn-2, dn-1, dn) is the transmit information or data sequence. In equation (5), three parameters q(xe2x80xa2), L, and h determine (establish) the specific CPM modulation scheme being used, wherein q(xe2x80xa2) is the phase pulse, L is the duration of the phase pulse, and h is the modulation index. Substituting the definition of the transmitted signal of equation (5) into the partial derivative of equation (4) one obtains equation (6) of FIG. 1. Ignoring the constants, the likelihood equation associated with equation (6) is equation (7) of FIG. 1.
Improved phase tracking method and apparatus are desired.
A method, according to an aspect of the invention, for establishing a phase reference signal for demodulating signals which are CPM modulated onto a carrier, includes the step of trellis demodulating received modulated signals using phase reference signal and symbol timing estimates, by calculating branch metrics signals representative of the likelihood that the branch was in the modulator path. The branch metrics signals are used to select the path through the trellis having the highest probability, representing a best estimate of the modulation signals. The branch metrics signals are phase shifted by xcfx80/2, to thereby generate phase shifted branch metrics signals associated with each path. At each symbol interval, the phase shifted branch metric associated with that one of the paths having the highest probability is selected. The selected phase shifted branch metric is used to adjust the value of the phase reference signals.
An apparatus according to an aspect of the invention, for demodulating data signals CPM modulated onto a carrier, includes a source of phase reference signals and a source of symbol timing estimates. A trellis demodulator is coupled to the source of phase reference signals and to the source of symbol timing estimates, for demodulating received modulated signals using the phase reference signals together with the symbol timing estimates, by calculating branch metrics signals representative of the likelihood that the branch was in the modulator path. A phase shifter phase shifts the branch metrics signals by xcfx80/2, to thereby generate phase shifted branch metrics signals associated with each path. A decoder using the branch metrics signals selects the path through the trellis having the highest probability. This path represents a best estimate of the data signals. The decoder also, at each symbol interval, for that one of the paths having the highest probability, selects or outputs the associated phase shifted branch metric. An adjustment arrangement is coupled to the source of phase reference signals and to the decoder, for applying the selected phase shifted branch metric to adjust the value of the phase reference signals. In a particular version of this aspect of the invention, the adjustment means comprises selected phase shifted branch metric signal smoothing means, which may include a low-pass filter.
According to another aspect of the invention, a method for establishing a phase reference signal for demodulating received data signals CPM modulated onto a carrier includes the step of trellis demodulating received modulated signals using a phase reference signal and symbol timing estimates. The step of trellis demodulating includes the calculation of branch metrics signals representative of the likelihood that the branch was in the modulator path, to ultimately produce estimated data signals. The method according to this other aspect of the invention further includes the estimation of least a form of the transmitted signal from the estimated data, the phase reference signal and the symbol timing estimates. The xe2x80x9cform of the transmitted signal,xe2x80x9d in this context, means a signal similar to the transmitted signal, but which may be at a downconverted frequency, or at baseband, rather than at a carrier frequency. The method includes the step of phase shifting the form of the transmitted signal, to thereby produce phase-shifted estimated transmitted signals. The phase-shifted estimated transmitted signals are correlated with at least a form of the received data signals, to produce phase error signals, and the phase error signals are applied or used to correct the phase reference signal. In this particular aspect of the invention, the phase error signals are smoothed before the step of applying. In another mode of this particular aspect of the invention, the phase shift is in the amount of xcfx80/2.
An apparatus, according to another avatar of the invention, for demodulating received data signals CPM modulated onto a carrier, includes a controllable source of phase reference signals and a source of symbol timing estimates. A trellis demodulator is coupled to the source of phase reference signals and to the source of symbol timing estimates, for demodulating at least signals having the same form, (but not necessarily the same frequency (ies)) as the received data signals modulated onto a carrier, using the phase reference signals together with the symbol timing estimates. The trellis demodulator does this by calculating branch metrics signals representative of the likelihood that the branch was in the modulator path, to thereby generate estimated data signals. A transmitter signal reconstituting arrangement is coupled to the trellis demodulator for receiving the estimated data signals, to the source of phase reference signals, and to the source of symbol timing estimates, for generating an estimate of the transmitted signals. A phase shifter is coupled to the transmitter signal reconstituting arrangement, for phase shifting the estimate of the transmitted signals by xcfx80/2, to thereby generate phase shifted estimated transmitted signals. A correlator is coupled to the phase shifter for receiving the phase shifted estimated transmitted signals, and the correlator is also coupled to receive the signals having the same form as the received data signals modulated onto a carrier, for correlating the phase shifted estimated transmitted signals with the signals having the same form as the received data signals modulated onto a carrier, to thereby produce a phase error signal. An adjustment arrangement is coupled to the correlator and to the source of phase reference signals, for applying the phase error signals to the source of phase reference signals, for adjusting the value of the phase reference signals.